It’s not news that the default palette for Flash is dreadful. There’s not much that you can do with this, other than pretend it’s not there:
I made my own early in the 2000s; it’s much more subdued (maybe a bit too subdued) but you’ll find it much more useful than the default. Here’s an empty Flash file containing my personalised flash palette. It was created in Macromedia Flash MX, so it’ll work with very old versions, and will open with all the later ones. Macromedia MX Screenshot:
All you need to do is download the .fla file, open it, then in the color swatch window, do this (note that this screenshot is Flash CS 5.5, all versions are much the same):
Once you save this palette as the default, any future .fla files that you open will have that new palette. If you ever want the old, ugly palette back, open that same swatch panel and select ‘Web 216’, and party like it’s 1999.
Notice that there’s a top row of green, blue, tan, turquoise, etc. I reserve these for layer colours, as you can see layers in outline mode very clearly when these colours are applied.
This is also the palette that I use in all my Lynda courses…so if you want to follow along with those, it’s a very handy thing to have.